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A generalized Kantorovich theorem for nonlinear equations based on function splitting

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Abstract

The Kantorovich theorem is a fundamental tool in nonlinear analysis for proving the existence and uniqueness of solutions of nonlinear equations arising in various fields. In the present paper we formulate and prove a generalized Kantorovich theorem that contains as special cases the Kantorovich theorem and a weak Kantorovich theorem recently proved by Uko and Argyros. An illustrative example is given to show that the new theorem is applicable in some situations in which the other two theorems are not applicable.

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Authors and Affiliations

  1. Department of Science and Mathematics, Johnson C. Smith University, Charlotte, NC, 28216, USA

    Livinus U. Uko & Ioannis K. Argyros

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  1. Livinus U. Uko
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  2. Ioannis K. Argyros
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Correspondence to Ioannis K. Argyros.

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Uko, L.U., Argyros, I.K. A generalized Kantorovich theorem for nonlinear equations based on function splitting. Rend. Circ. Mat. Palermo 58, 441–451 (2009). https://doi.org/10.1007/s12215-009-0034-y

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  • DOI: https://doi.org/10.1007/s12215-009-0034-y

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